Maximal independent sets in Borel graphs and large cardinals
Haim Horowitz, Saharon Shelah
TL;DR
This paper constructs a Borel graph whose properties regarding maximal independent sets are equiconsistent with the existence of an inaccessible cardinal, linking descriptive set theory with large cardinal axioms.
Contribution
It establishes a novel connection between Borel graph properties and large cardinal axioms, specifically showing the equiconsistency with inaccessible cardinals.
Findings
Constructed a Borel graph with specific independence properties.
Linked the non-existence of maximal independent sets to large cardinal axioms.
Demonstrated equiconsistency between set-theoretic axioms and graph properties.
Abstract
We construct a Borel graph G such that ZF+DC+"There are no maximal independent sets in G" is equiconsistent with ZFC+"There exists an inaccessible cardinal".
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Taxonomy
TopicsAdvanced Topology and Set Theory · Limits and Structures in Graph Theory · Computability, Logic, AI Algorithms